Internal problem ID [9181]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1602.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 a^{10} y^{11}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 61
dsolve(diff(diff(y(x),x),x)+(5+1)*a^(2*5)*y(x)^(2*5+1)-y(x)=0,y(x), singsol=all)
\begin{align*} \int _{}^{y \relax (x )}\frac {1}{\sqrt {-\textit {\_a}^{12} a^{10}+\textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {1}{\sqrt {-\textit {\_a}^{12} a^{10}+\textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.385 (sec). Leaf size: 49
DSolve[-y[x] + a^(2*5)*(1 + 5)*y[x]^(1 + 2*5) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+2 \left (\frac {K[1]^2}{2}-\frac {1}{2} a^{10} K[1]^{12}\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]